I am interested in counting the number of times a given part (some integer) occurs in the weak compositions (i.e. 0 is admitted as a summand) of some restricted size and some restricted maximum summand.
E.G., in the compositions of 10 of length 4 with a maximum of 5 allowed for summands, how many times does some integer x occur?
A scan of my texts yielded generating functions for unrestricted compositions, but no joy for my needs.
Any references to texts/papers appreciated.